Geometry & Topology Volume 13, issue 3 (2009)

We classify abelian subgroups of Out(F_n) up to finite index in an algorithmic and computationally friendly way. A process called disintegration is used to canonically decompose a single rotationless element ϕ into a composition of finitely many elements and then these elements are used to generate an abelian subgroup A(ϕ) that contains ϕ. The main theorem is that up to finite index every abelian subgroup is realized by this construction. As an application we give an explicit description, in terms of relative train track maps and up to finite index, of all maximal rank abelian subgroups of Out(F_n) and of IA_n.

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Keywords

outer automorphism, free group, train track

Mathematical Subject Classification

Primary: 20F65

Secondary: 20F28

References

Publication

Received: 21 February 2007
Revised: 25 February 2009
Accepted: 7 March 2008
Published: 5 March 2009
Proposed: Benson Farb
Seconded: Martin Bridson, Joan Birman

Authors

Mark Feighn
Math Department Rutgers University Newark, NJ 07102 USA

Michael Handel
Math Department Lehman College Bronx, NY 10468 USA